We optimize \(F_{\lambda ,{w^1},{w^2}}\)  using FW-smoothing with \(\beta _0=100\)  and \(T=5k\)  for Lastfm-2k, and \(\beta _0=1000\)  and \(T=50k\)  for MovieLens. \(F^{\it welf} \)  and \(F^{\rm eq}\)  are optimized with the Frank-Wolfe method of [1]} for \(T=1k\)  and \(T=5k\)  iterations respectively for Lastfm-2k and MovieLens. This is the number of iterations recommended by [1]}, while we need more interactions for FW-smoothing because its convergence is \(O(\frac{1}{\sqrt{T}})\)  rather than \(O(\frac{1}{T})\)  because of non-smoothness.
